2.2 THE ORPD PROBLEM FORMULATION The objective of the ORPD is to minimize the active power loss in the transmission netw

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2 2 The Orpd Problem Formulation The Objective Of The Orpd Is To Minimize The Active Power Loss In The Transmission Netw 1 (34.44 KiB) Viewed 44 times

2 2 The Orpd Problem Formulation The Objective Of The Orpd Is To Minimize The Active Power Loss In The Transmission Netw 2 (28.54 KiB) Viewed 44 times

2.2 THE ORPD PROBLEM FORMULATION The objective of the ORPD is to minimize the active power loss in the transmission network, which can be described as follows: Minimize f(x, u) (1) while satisfying (2) g(x, u)-0 h(x, w) ≤0 (3) 13 where f(x, u) is the objective function to be optimized, gs. a) and hx, a are the set of equality and inequality constraints respectively. x is a vector of state variables, and a is the vector of control variables. The state variables are the load bus (PQ bus) voltages, phase angles, generator bus voltages and the slack active generation power. The control variables are the generator bus voltages, the shunt capacitors/reactors and the transformers tap settings. The objective function of the ORPD is to minimize the active power losses in the transmission lines/network, which can be defined as follows: Ni F-Min. PG₁[V+V-2V/V, costő, – d)] where k refers to the branch between buses i and j; P and G, are the active loss and mutual conductance of branch & respectively, d, and d, are the voltage angles at bus i and j. Ne is the total number of transmission lines. The above minimization objective function is subjected to the both equality and inequality constraints. 2.2.1 EQUALITY CONSTRAINTS The equality constraints are the load flow equations given as: N₂ (5) Par-P-VVG, cos(-6) + B₁ sinfo-6-0 F1 Na QG-Q-VVG, sinfd-6)+ B, cos(6,-61-0 (6) whana D and. Aan the activa und. canotion tical D.

23:13 X dissertation_agbugba_ee Poslospo Ne (9) where N is the number of reactive compensation devices 3) Transformer Constraints: Tap settings are restricted by the upper and lower bounds on the transformer tap ration: T. ST. ST.** PLN (10) where Ny is the number of transformers 2.2.3 PENALTY FUNCTION The most efficient and easiest way to handle constraints in optimization problems is by the use of penalty functions. The direction of the search process and thus, the quality of the optimal solution are hugely impacted by these functions. A suitable penalty function has to be choses in onder to solve a particular problem. The main goal of a penalty fimction is to maintain the systems security These penalty functions are associated with numerous mer defined coefficiens which have to be rigorously tuned to suit the given problem. This research used a quadratic penalty function method in which a penalty term is added to the objective function for any violation of contraints. The inequality constraints which include the generater constraints, reactive compensation srces and transformer constraints are combined into the objective function as a penalty tem, while the equality constraints and generator reactive power limits are satisfied by the Newton-Raphwn load flow method. By adding the inequality constraints to the objective function Fin Eq. 14), the augmented objective function F to be minimized becomes 1₁-1² + 2 (0₂-0₂ ²7² +2+ (- (11) Ty where we are the penalty factors, and 1, Q., and are defined V 1, -- -{X- (12) fe-:00 la-ive-a- (13) 0. -{ •T:UT.>7.- Bu miss the wase of the master fton method 1611 the al T- (14) 15